Identify the surface with the given vector equation. r(u, v) = 2 sin(u) i + 5 cos(u) j + v k, 0 ≤ v ≤ 5 plane hyperbolic paraboloid circular paraboloid elliptic cylinder circular cylinder

Note that this just produces three parametric equations:





In the plane, this is just he parametric equation for an ellipse (as a function of u). The z is simply a linear function. 

The surface is then an ellipse extruded along the z-axis. We get a elliptic cylinder.